Course taught by Prof. Sotos.
Textbooks
- https://utstat.utoronto.ca/mikevans/jeffrosenthal/
- https://drive.google.com/file/d/1VmkAAGOYCTORq1wxSQqy255qLJjTNvBI/edit
Notes
- Take-home quizes
- Office hours TUES, THURS 1-3pm IA4072
- 15% quiz best 9/11
- Term test 1 20% (Week 1-4)
- Formula sheet will be handed out
- A tiny bit of expectations questions
- Term test 2 20% (Week 5-8)
- Final 45%
- Problem-set and solution set will be posted each week
Concepts
Week 1
- Probability Model
- Naive Set Theory
- Probability
- Experiment
- Outcome
- Sample Space
- Event
- Tuple
- Venn Diagrams
- Probability Function
- Probability Axioms
- Probability Model
- Probability Rules
- Subset
- Disjoint
- Partition
- Discrete Sample Space
- Discrete Uniform Probability Space
- Counting
- Partial Derivative
- Jacobian Matrix
- Multiple Integral
- Change of Order of Integration
- Change of Integration Variables
Week 2
- Conditional Probability
- Bayesian Statistics
- Conditional Probability Axioms
- Regular Probability Theorem
- Bayes Theorem
- Prevalence of Condition
- Finding Unconditional Probability from Conditional Probabilities Example
- Multinomial Coefficient
- Independent Events
- Mutual Independence
- Conditioning on Multiple Events
- Pairwise Independence
- Pairwise Independence Does Not Imply Mutual Independence
- Multiplication Rule of Probability
- Conditional Independence
Week 3
- Random Variable
- Probability Distribution
- Functions of Random Variables
- Probability Mass Function
- Probability Density Function
- Cumulative Distribution Function
- PMF From CDF
- PDF From CDF
- CDF and RDF Example
- Bernoulli Random Variables
- Bernoulli Distribution
- Binomial Random Variable
- Binomial Distribution
- Binomial Theorem
- Hypergeometric Distribution
Week 4
- Expectations
- Geometric Distribution
- Geometric Series
- Negative Binomial Distribution
- Poisson Distribution
- Variance
- Urn Problem
- Binomial Formulas